Theorem 19.41vv

Version of 19.41 with two quantifiers and a disjoint variable condition requiring fewer axioms. (Contributed by NM, 30-Apr-1995.)

Conclusion
\( \vdash \exists x \, \exists y \, (\varphi \wedge \psi) \leftrightarrow \exists x \, \exists y \, \varphi \wedge \psi \)
Proof
19.41v
l1
exbii _
\( \vdash \exists x \, \exists y \, (\varphi \wedge \psi) \leftrightarrow \exists x \, (\exists y \, \varphi \wedge \psi) \)
19.41v
\( \vdash \exists x \, (\exists y \, \varphi \wedge \psi) \leftrightarrow \exists x \, \exists y \, \varphi \wedge \psi \)
bitri l1 _